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Cohesion and tensile properties of W-TiC interface under irradiation
Fusion Engineering and Design 149 (2019) 111353
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Cohesion and tensile properties of W-TiC interface under irradiation L.C. Liu, J.L. Fan, H.R. Gong
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T
State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan, 410083, China
A R T I C LE I N FO
A B S T R A C T
Keywords: W-TiC interface Irradiation Cohesion properties Tensile properties First- principle calculations
First principles calculation reveals that the formation of the TiC(001)/W(001) interface could increase the tensile strength of W, which is due to the stronger W-W bond in the interface than that in W bulk. Interestingly, the descending sequence of the bonding strength of the bonds in the interface is as follows: W-C → W-W →Ti-C, and the Ti-C bond in the interface is weaker than that in TiC bulk. It is also found that irradiation has an important effect to reduce cohesion strength, interface stability, and tensile strength of the TiC(001)/W(001) interface, and that such an effect is mainly attributed to the debonding of the W-C and Ti-C bonds as a result of the formation of carbon clusters due to irradiation. Furthermore, the addition of TiC could improve the tensile strength of W after irradiation under tensile loading along the direction parallel to the interface, while decrease the tensile strength of irradiated W under tensile loading along the direction perpendicular to the interface.
1. Introduction Tungsten (W) has been well considered as a promising candidate material for plasma facing materials (PFM) in future fusion reactors, owing to its high melting point, nice thermal conductivity, excellent high-temperature strength, low thermal expansion coefficient, and low sputtering yield, etc. [1–18]. Nevertheless, the main drawbacks of tungsten such as low temperature or recrystallization brittleness, high ductile-brittle transition temperature (DBTT), and irradiation embrittlement [3–5,8–10,12,19–21], seriously limit the applications of W materials. One of effective approaches to solve the above problems is to add some dispersed second phase particles in the W matrix, and TiC is well regarded as one of the effective second phase particles to significantly improve the mechanical properties, resistance to irradiation, and ductility of W matrix [3,6,12,22–36]. It is well believed that W-TiC interface plays an important role in mechanical properties of various W products. Regarding the tensile properties of the W-TiC system, there are already some experimental investigations in the literature [2,4,8–10]. For instance, Lang et al. found that the addition of TiC particles could decrease the tensile strength and increase the elongation of W at 300 ℃ [2]. On the contrary, Browning et al. discovered that TiC could significantly increase the tensile strength of W, while bring an obvious decrease of ductility up to the temperature of 1926 ℃ [9]. Further theoretical studies are therefore needed to clarify such a controversy. In addition, a lot of researches have demonstrated that irradiation resistance of tungsten alloys can be significantly improved by the
⁎
addition of TiC particles in tungsten matrix [3,6,7,12,22–26]. Specifically, these scientific reports in the literature are principally concentrated on microstructures and hardening/embrittlement, i.e., a fewer radiation-induced defects, a lower density of blisters and a lower surface cracks [3,7,12,22,24,25], the decrease of radiation hardening [3,6,7,24,26], and the improved resistance to recrystallization embrittlement [6,7,23]. Nevertheless, regarding the cohesion and tensile properties of W-TiC system after irradiation, there is not any report so far in the literature. By means of first-principle calculations based on density functional theory [37,38], the present study is, therefore, dedicated to systematically investigate the stress-strain behaviors of W-TiC interface as well as the effects of irradiation on cohesion and tensile properties of W-TiC interface. Accordingly, the W-TiC interface with the (001)/(001) orientation is purposely chosen in the present study, as this interface has a very small mismatch of 3.396% and has been observed through experimental investigations [8]. It will be shown that the present results agree well with experimental observations in the literature, and the intrinsic mechanism will be revealed in terms of electronic structures and atomic bonding, which could provide a deep understanding regarding cohesion and tensile properties of W-TiC interface under irradiation. 2. Method of calculation The present first principle calculations are carried out using Vienna ab initio simulation package (VASP) [37,38] based on density functional
Corresponding author. E-mail address: [email protected] (H.R. Gong).
https://doi.org/10.1016/j.fusengdes.2019.111353 Received 11 July 2019; Received in revised form 31 August 2019; Accepted 29 September 2019 Available online 09 October 2019 0920-3796/ © 2019 Elsevier B.V. All rights reserved.
Fusion Engineering and Design 149 (2019) 111353
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¯
Fig. 1. (a) Three dimensional model and (b) x–y projection of the TiC(001)/W(001) interface. The x-axis is [100]W and [110]TiC, the y-axis is [010]W and [1 10]TiC, and the z-axis is [001]W and [001]TiC. The gray, brown, and blue spheres represent W, C, and Ti atoms, respectively.
3. Results and discussions
theory with the projector-augmented wave (PAW) method [39,40]. The exchange-correlation function is described by generalized gradient approximation (GGA) of Perdew-Burke-Enzerof (PBE) [41], and the cutoff energy of plane wave basis is 500 eV. The periodic boundary conditions are applied in three directions of the unit cell. The temperaturesmearing method of Methfessel-Paxton [42] with the energy convergence criteria of 0.01 meV and the tetrahedron method of Blöchl [43] with the energy convergence criteria of 0.001 meV are used for relaxation and static calculations, respectively. Accordingly, a 3 × 3 interface unit cell with six substrate layers (W) and six overlayers (TiC) are chosen for the TiC(001)/W(001) interface. The optimized bulk lattice constant (3.176 Å) of the substrate (W) and its BCC structure are chosen for the interface. Namely, the present TiC(001)/W(001) interface model has a unit size of 9.528 × 9.528 × 22.508 Å3 with 162 atoms, which are shown clearly in Fig. 1. For the TiC(001)/W(001) interface, the x-axis is [100]W and
3.1. Stress-strain behaviors of W-TiC interfaces It is commonly believed that the addition of TiC particles in tungsten matrix might effectively change the mechanical properties of W. As mentioned above, there are already some theoretical and experimental investigations regarding mechanical properties of the W-TiC system in the literature [2,4,8–10], while the relative magnitude of the tensile strength of the W-TiC interface from several experimental observations in the literature are quite different from each other [2,8,9], i.e., the tensile strength of W-TiC is observed to be higher [8,9] and lower [2] than that of pure W, respectively. It is, therefore, of importance to theoretically investigate this issue. After a series of calculations, Fig. 2 shows the obtained stress-strain curves of the TiC(001)/W(001) interface under tensile loading along the x ([100]W and [110]TiC) and z ([001]W and [001]TiC) directions, respectively. The corresponding curves of BCC W and B1 TiC bulks are also included in Fig. 2 for the sake of comparison. It should be pointed out that the stress-strain curve of the TiC(001)/W(001) interface, BCC W, or B1 TiC under tensile loading along the y direction is not shown, as it is equivalent to that along the x direction due to structural symmetry. One can observe from Fig. 2 that the tensile strength of W under phonon instability is very close to the climax of the stress-strain curve, suggesting that the effect of phonon instability on the ideal tensile strength of W could be neglected. On the contrary, the tensile strength of TiC caused by phonon instability along the x or z direction is lower than the corresponding ideal strength at the climax of the stress-strain curve. This feature indicates that the effect of phonon instability on the tensile strength of TiC is bigger than that of W. It should be pointed out that the obtained tensile stress of BCC W bulk along the x direction under phonon instability from the present study are 28.832 GPa, which agrees well with the corresponding calculated value of 28.86 GPa in the literature [50]. In addition, the tensile strength and critical strain of the TiC(001)/ W(001) interface along the x direction is apparently bigger than those along the z direction. Interestingly, such a feature can be also seen in B1 TiC bulk, while the stress-train curves of BCC W along the x and z directions are exactly the same due to crystal symmetry. This comparison therefore suggests that the addition of TiC fundamentally brings about the differences of the stress-strain curves of the TiC(001)/W(001) interface along the x and z directions. It could be also discerned from Fig. 2 that the critical stress of the TiC(001)/W(001) interface caused by phonon instability along the x direction is 38.596 GPa, considerably bigger than the corresponding value of 28.832 GPa for BCC W. The critical stress (30.420 GPa) of the
¯
[110]TiC, the y-axis is [010]W and [1 10]TiC, and the z-axis is [001]W and [001]TiC. Moreover, a unit cell of 4 × 4 × 4 is also constructed for BCC W and B1 TiC (a = 4.339 Å) bulks with similar settings of the above interface for the sake of comparison. For the TiC(001)/W(001) interface, the Monkhorst-Pack k-meshes of 1 × 1 × 1 and 5 × 5×5 are chosen for relaxation and static calculations, respectively. Accordingly, the interval of the tensile strain for the TiC(001)/W(001) interface is 0.01 and the stress-strain curve is derived by means of incrementally deforming the structures along the strain direction. At the same time, both the atomic basis vectors orthogonal to the applied strain and the atoms are relaxed. To ensure the continuous path of strain, the starting position at each strain step is taken from the relaxed coordinates of the previous step [44]. In order to verify the lattice instability during the process of tensile strain, the phonon spectra of both W and TiC are calculated by means of density functional perturbation theory (DFPT) method [45]. To simulate the irradiation in the interface area and keep the system from melting, the primary knock-on atom (PKA) is initiated by assigning a kinetic energy of 90 eV [46] to a W atom in the 6th layer of interface, and the moving direction of the PKA is toward the TiC lattice. Such a setting is mainly due to the well-known fact that the irradiation induced cascade in the W-TiC interface would be triggered from the dominant W phase in the actual situations [47]. After a series of test calculations, the micro-canonical ensemble (NVE) ensemble with 1000 fs is used for PKA simulations. To simulate the cohesion properties and ideal tensile properties of the interface after irradiation, the Langevin thermostat method [48,49] is used for annealing simulations from the stable temperature to 0 K. The canonical ensemble (NVT) with 1000 fs at 0 K is then performed for thermal treatment.
2
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Fig. 2. The stress-strain curves of the TiC(001)/W(001) interface along (a) the x direction ([100]W and [110]TiC) and (b) z direction ([001]W and [001]TiC) before irradiation. The corresponding curves of BCC W and B1 TiC bulks are also included for comparison.
strength of the bonds in the interface is as follows: W-C → W-W →Ti-C. In addition, the bonding strength of W-W in the interface should be stronger than that in W bulk, whereas the Ti-C bond in the interface is weaker than that in TiC bulk. Such a stronger W-W bond due to the interface formation fundamentally brings about the higher tensile strength of the W-TiC interface than those of BCC W, as shown in Fig. 2. Furthermore, Fig. 4 shows the affine deviation of W-W, Ti-C, and WC bond lengths in the TiC(001)/W(001) interface as a function of tensile strain along the z direction ([001]W and [001]TiC). It should be noted that the affine deviation is defined as the difference between the real displacement and affine displacement, and the positive value indicates that the interaction of atoms is weakened, vice versa. One can see from this figure that the affine deviation of Ti-C bond length in the interface experiences an increase as an increase of the tensile strain, while the affine deviation of W-W or W-C bond length decreases with the increase of the tensile strain. Such an opposite trend of affine deviation would be
interface along the z direction is also slightly bigger that that (28.832 GPa) of BCC W. The above features indicate that the formation of the W-TiC interface should increase the tensile strength of W, which matches well with similar experimental observations in the literature [8,9], while constrary to the other evidence from experiments [2]. According to our understanding, such an experiental controvery regarding tensile strength of W-TiC interface and BCC W might be probably due to experimental errors or contamination of the samples [2,8,9], and further experimental or theoretical studies are therefore welcome to handle this issue. To have a deep understanding of the stress-strain curves of W-TiC interfaces, Fig. 3 displays the charge density plots of TiC(001)/W(001) interface, B1 TiC bulk, and BCC W bulk. It can be discerned clearly from Fig. 3(a) that in the W-TiC interface area, the W-W bond is obviously less dense than the W-C bond, whereas denser than the Ti-C bond. This comparison indicates that the descending sequence of the bonding
Fig. 3. Charge density plots of (a) TiC(001)/W(001) interface, (b) B1 TiC bulk, and (c) BCC W bulk. 3
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Table 1 Interface energy and work of separation of TiC(001)/W(001) interface before and after irradiation. Also listed are the critical stresses of W and W-TiC interface before and after irradiation as well as the variation (Δσ ) of critical stress due to irradiation. Phases
Wsep
Eint 2
(J/m ) W
W-TiC
mainly due to the weaker Ti-C bond in the interface shown in Fig. 3(a). It therefore follows that when the tensile stress is added along the z direction perpendicular to the TiC(001)/W(001) interface, the strain would mainly happen in the TiC lattice and the final fracture should be also taken place in the TiC lattice, instead of the W lattice and W-TiC interface (figures not shown). 3.2. Cohesion and tensile properties of W-TiC interface under irradiation As mentioned above, some experimental investigations in the literature have already revealed that the addition of TiC particles could improve the irradiation resistance of tungsten alloys, i.e., the lower radiation-induced defects, lower density of blisters, lower surface cracks, and higher resistance to irradiation embrittlement and irradiation hardening [3,6,7,23,24,26]. As to the cohesion and tensile properties of W-TiC system after irradiation, however, there is not any report so far in the literature. The present first principles calculation is therefore dedicated to comparatively investigate the cohesion and tensile properties of W-TiC interface and pure W under irradiation. The work of separation (Wsep ) and interface energy (Eint ) of W-TiC interface before and after irradiation are first calculated by the following formulas [14,15]:
EW + ETiC − Etot 2A
(1)
Eint =
Etot − Ew − bulk − ETiC − bulk 2A
(2)
where EW and ETiC represent total energies of pure W and TiC surface layers after removing the TiC and W layers, respectively; Etot , Ew − bulk , and ETiC − bulk are total energies of TiC(001)/W(001) interface and bulk energies of W and TiC layers, respectively, and A is the area of the TiC(001)/W(001) interface. Consequently, the derived Wsep and Eint values of TiC(001)/W(001) interface before and after irradiation are summarized in Table 1. To find out the effects of irradiation on tensile properties of W-TiC interface, Fig. 5 displays the calculated stress-strain curves of W-TiC interface and W before and after irradiation upon tensile loading along the x ([100]W and [110]TiC) and z directions ([001]W and [001]TiC). The critical stresses of W and W-TiC interface from Fig. 5 are thus shown in Table 1. In addition, the variation (Δσ ) of critical stresses due to irradiation is defined as:
Δ σ=
σa − σb σb
5.220 4.640
(J/m )
0.865 2.285
x direction
z direction
28.832 24.377 −15.45% 38.596 27.094 −29.80%
28.832 24.377 −15.45% 30.420 20.535 −32.50%
values of Δσ values are also listed in Table 1. Several characteristics could be discerned from Fig. 5 and Table 1. Firstly, the Wsep value (4.640 J/m2) of the irradiated TiC(001)/W(001) interface becomes lower than the corresponding value of 5.220 J/m2 before irradiation, and the interface energy (2.285 J/m2) of the irradiated TiC(001)/W(001) interface is higher than that (0.865 J/m2) of the interface before irradiation. These comparisons imply that irradiation should have an important effect to reduce the cohesion strength and interface stability of the TiC(001)/W(001) interface. The fundamental mechanism of such a decrease will be revealed later in the following paragraphs. Secondly, the critical stresses and strains of both W-TiC interface and pure W after irradiation under tensile loading along the x or z direction are lower than the corresponding values before irradiation, respectively. In other words, irradiation would reduce tensile strength and ductility of both W-TiC interface and pure W. Interestingly, the decrease of critical stress (Δσ ) of the W-TiC interface due to irradiation seems much bigger than the corresponding value of pure W. Thirdly, the critical stress (27.094 GPa) of the W-TiC interface after irradiation under tensile loading along the x direction is higher than the corresponding value (24.377 GPa) of pure W. On the contrary, the critical stress (20.535 GPa) of the W-TiC interface after irradiation under tensile loading along the z direction is lower than the corresponding value (24.377 GPa) of pure W. These characteristics suggest that the addition of TiC could improve the tensile strength of W after irradiation under tensile loading along the direction parallel to the interface, while decrease the tensile strength of irradiated W under tensile loading along the direction perpendicular to the interface. It should be noted that the above observation is derived when the irradiation is performed under the low energy (90 eV) of PKA. It is of importance to have a deep understanding of the above theoretical observations in terms of atomic bonding. Accordingly, Fig. 6 shows the atomic configurations of the TiC(001)/W(001) interface after irradiation. One can observe clearly from this figure that some carbon clusters have been formed in the W-TiC interface due to irradiation, which is consistent with similar experimental observation in the literature [51]. These carbon clusters imply that some W-C and Ti-C bonds in the interface area shown in Fig. 3 should have been broken due to irradiation. Such a breaking of W-C bonds would intrinsically bring about the decrease of cohesion strength and interface stability of the W-TiC interface as mentioned above. The debonding of the Ti-C bonds due to irradiation should also induce a bigger decrease of critical stresses of the W-TiC interface as shown in Table 1. Finally, we turn to discuss a little bit about the different effects of TiC on tensile strength of irradiated W, i.e., the addition of TiC could increase the critical stress of irradiated W along the x direction parallel to the interface, whereas decrease the critical stress along the z direction perpendicular to the interface. According to our understanding, when loading is along the x direction parallel to the interface, the tensile strength of the W-TiC interface should be determined by the
Fig. 4. Affine deviation of W-W, Ti-C, and W-C bonds length in the TiC(001)/W (001) interface as a function of tensile strain along the z direction ([001]W and [001]TiC).
Wsep =
before irradiation after irradiation Δσ before irradiation after irradiation Δσ
Critical stress (GPa) 2
(3)
Where σa and σb are the critical stresses of W-TiC interface or pure W after and before irradiation, respectively. Consequently, the obtained 4
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Fig. 5. Stress-strain curves of W-TiC interface and W before and after irradiation upon tensile loading along the (a) x direction ([100]W and [110]TiC) and (b) z direction ([001]W and [001]TiC).
Fig. 6. Atomic configurations of the TiC(001)/W(001) interface after irradiation. The gray, brown, and blue spheres represent W, C, and Ti atoms, re¯
spectively. The x-axis is [100]W and [110]TiC, the y-axis is [010]W and [1 10]TiC, and the z-axis is [001]W and [001]TiC.
strong phase (TiC) as W and TiC are forced to deform together [47,52]. That is to say, the much higher strength of TiC along the x direction shown in Fig. 2(a) fundamentally brings about the increase of the tensile strength of irradiated W along the x direction. On the other hand, when loading is along the z direction perpendicular to the interface, the deformation of the W-TiC interface occurs mainly in the TiC part, and Fig. 7 displays the fracture position of TiC in the TiC(001)/W(001) interface after irradiation upon tensile loading along the z direction at a strain of 12.683%. Such a failure of TiC in the W-TiC interface along the z direction would be mainly attributed to the very close tensile strength of W and TiC shown in Fig. 2(b), the weaker Ti-C bond in the interface area revealed from Fig. 3, and the breaking of some Ti-C bonds due to irradiation displayed in Fig. 6. It therefore follows that the irradiated TiC should be weaker than the irradiated W in the W-TiC interface upon loading along the z direction, and the weaker TiC intrinsically causes the decrease of tensile strength of W along the z direction.
Fig. 7. Atomic configurations of the TiC(001)/W(001) interface after irradiation upon tensile loading along the z direction ([001]W and [001]TiC) at a strain of 12.683%. The gray, brown, and blue spheres represent W, C, and Ti atoms, respectively.
4. Conclusions First-principle calculations have been used to investigate the stressstrain behaviors of W-TiC interface as well as the effects of irradiation on cohesion and tensile properties of W-TiC interface. It is found that the formation of the W-TiC interface increases the tensile strength of W due to a stronger W-W bond in the interface, and the W-W bond is weaker and stronger than the W-C and Ti-C bonds in the interface area, respectively. Irradiation would reduce tensile strength of both W-TiC interface and pure W, while the decrease of critical stress of the W-TiC interface due to irradiation seems much bigger than that of pure W. Interestingly, TiC could increase and decrease the tensile strength of W 5
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after irradiation under tensile loading along the x and z directions, respectively. The derived results are in good agreement with experimental observations in the literature, and the intrinsic mechanism has been revealed in terms of electronic structure and atomic bonding, which could provide a deep understanding regarding cohesion and tensile properties of W-TiC interface under irradiation.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This research work was supported by National Natural Science Foundation of China (Grant No. 51534009), Project supported by the Fundamental Research Funds for the Central Universities of Central South University (No. 2018zzts126) and Project supported by State Key Laboratory of Powder Metallurgy, Central South University, Changsha, China. References [1] Z. Oksiuta, K. Perkowski, M. Osuchowski, M. Zalewska, M. Andrzejczuk, Microstructure and thermal properties of mechanically alloyed W-1% TiC powder consolidated via two-step HIPping, Fusion Eng. Des. 126 (2018) 51–58. [2] S. Lang, Q. Yan, N. Sun, X. Zhang, L. Deng, Y. Wang, C. Ge, Microstructure, basic thermal–mechanical and Charpy impact properties of W-0.1 wt.% TiC alloy via chemical method, J. Alloys. Compd. 660 (2016) 184–192. [3] H. Kurishita, Y. Amano, S. Kobayashi, K. Nakai, H. Arakawa, Y. Hiraoka, T. Takida, K. Takebe, H. Matsui, Development of ultra-fine grained W–TiC and their mechanical properties for fusion applications, J. Nucl. Mater. 367 (2007) 1453–1457. [4] H. Kurishita, S. Matsuo, H. Arakawa, M. Narui, M. Yamazaki, T. Sakamoto, S. Kobayashi, K. Nakai, T. Takida, K. Takebe, High temperature tensile properties and their application to toughness enhancement in ultra-fine grained W-(0-1.5) wt % TiC, J. Nucl. Mater. 386 (2009) 579–582. [5] S. Lang, Q. Yan, N. Sun, X. Zhang, C. Ge, Effects of TiC content on microstructure, mechanical properties, and thermal conductivity of W-TiC alloys fabricated by a wet-chemical method, Fusion Eng. Des. 121 (2017) 366–372. [6] H. Kurishita, S. Matsuo, H. Arakawa, T. Sakamoto, S. Kobayashi, K. Nakai, T. Takida, M. Kato, M. Kawai, N. Yoshida, Development of re-crystallized W–1.1%TiC with enhanced room-temperature ductility and radiation performance, J. Nucl. Mater. 398 (2010) 87–92. [7] M. Fukuda, A. Hasegawa, T. Tanno, S. Nogami, H. Kurishita, Property change of advanced tungsten alloys due to neutron irradiation, J. Nucl. Mater. 442 (2013) S273–S276. [8] S. Miao, Z. Xie, T. Zhang, X. Wang, Q. Fang, C. Liu, G. Luo, X. Liu, Y. Lian, Mechanical properties and thermal stability of rolled W-0.5 wt% TiC alloys, Mater. Sci. Eng., A 671 (2016) 87–95. [9] P.N. Browning, S. Alagic, A. Kulkarni, L. Matson, J. Singh, Room and ultrahigh temperature structure-mechanical property relationships of tungsten alloys formed by field assisted sintering technique (FAST), Mater. Sci. Eng., A 674 (2016) 701–712. [10] X.Y. Tan, P. Li, L.M. Luo, Q. Xu, K. Tokunaga, X. Zan, Y.C. Wu, Effect of secondphase particles on the properties of W-based materials under high-heat loading, Nucl. Mater. Energy 9 (2016) 399–404. [11] C.Y. Wu, L. Sun, C.P. Liang, H.R. Gong, M.L. Chang, D.C. Chen, Electronic structures and thermoelectric properties of polytype phases of bismuth, J. Phys. Chem. Solids 134 (2019) 52–57. [12] Q. Xu, X.Y. Ding, L.M. Luo, M. Miyamoto, M. Tokitani, J. Zhang, Y.C. Wu, Thermal stability and evolution of microstructures induced by He irradiation in W–TiC alloys, Nucl. Mater. Energy 15 (2018) 76–79. [13] L. Chen, L. Xiong, D.S. Li, H.R. Gong, First-principles calculation of Zr doping on cohesion properties of TiC/W interfaces, Fusion Eng. Des. 125 (2017) 85–88. [14] J.W. Wang, J.L. Fan, H.R. Gong, Effects of Zr alloying on cohesion properties of Cu/ W interfaces, J. Alloys. Compd. 661 (2016) 553–556. [15] D.Y. Dang, L.Y. Shi, J.L. Fan, H.R. Gong, First-principles study of W–TiC interface cohesion, Surf. Coat. Technol. 276 (2015) 602–605. [16] L. Chen, W. Qian, X. Lei, H.R. Gong, Mechanical properties and point defects of MC (M=Ti, Zr) from first-principles calculation, J. Alloys. Compd. 747 (2018) 972–977. [17] L.C. Liu, H.R. Gong, S.F. Zhou, X. Gong, Adsorption, diffusion, and permeation of hydrogen at PdCu surfaces, J. Membr. Sci. (2019) 117206. [18] J. Qian, C.Y. Wu, H.R. Gong, S.F. Zhou, Cohesion properties of W-ZrC interfaces from first principles calculation, J. Alloys. Compd. 768 (2018) 387–391. [19] Q.Y. Hou, L.M. Luo, Z.Y. Huang, P. Wang, T.T. Ding, Y.C. Wu, Comparison of W–TiC composite coatings fabricated by atmospheric plasma spraying and supersonic atmospheric plasma spraying, Fusion Eng. Des. 105 (2016) 77–85.
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Cohesion and tensile properties of W-TiC interface under irradiation L.C. Liu, J.L. Fan, H.R. Gong
⁎
T
State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan, 410083, China
A R T I C LE I N FO
A B S T R A C T
Keywords: W-TiC interface Irradiation Cohesion properties Tensile properties First- principle calculations
First principles calculation reveals that the formation of the TiC(001)/W(001) interface could increase the tensile strength of W, which is due to the stronger W-W bond in the interface than that in W bulk. Interestingly, the descending sequence of the bonding strength of the bonds in the interface is as follows: W-C → W-W →Ti-C, and the Ti-C bond in the interface is weaker than that in TiC bulk. It is also found that irradiation has an important effect to reduce cohesion strength, interface stability, and tensile strength of the TiC(001)/W(001) interface, and that such an effect is mainly attributed to the debonding of the W-C and Ti-C bonds as a result of the formation of carbon clusters due to irradiation. Furthermore, the addition of TiC could improve the tensile strength of W after irradiation under tensile loading along the direction parallel to the interface, while decrease the tensile strength of irradiated W under tensile loading along the direction perpendicular to the interface.
1. Introduction Tungsten (W) has been well considered as a promising candidate material for plasma facing materials (PFM) in future fusion reactors, owing to its high melting point, nice thermal conductivity, excellent high-temperature strength, low thermal expansion coefficient, and low sputtering yield, etc. [1–18]. Nevertheless, the main drawbacks of tungsten such as low temperature or recrystallization brittleness, high ductile-brittle transition temperature (DBTT), and irradiation embrittlement [3–5,8–10,12,19–21], seriously limit the applications of W materials. One of effective approaches to solve the above problems is to add some dispersed second phase particles in the W matrix, and TiC is well regarded as one of the effective second phase particles to significantly improve the mechanical properties, resistance to irradiation, and ductility of W matrix [3,6,12,22–36]. It is well believed that W-TiC interface plays an important role in mechanical properties of various W products. Regarding the tensile properties of the W-TiC system, there are already some experimental investigations in the literature [2,4,8–10]. For instance, Lang et al. found that the addition of TiC particles could decrease the tensile strength and increase the elongation of W at 300 ℃ [2]. On the contrary, Browning et al. discovered that TiC could significantly increase the tensile strength of W, while bring an obvious decrease of ductility up to the temperature of 1926 ℃ [9]. Further theoretical studies are therefore needed to clarify such a controversy. In addition, a lot of researches have demonstrated that irradiation resistance of tungsten alloys can be significantly improved by the
⁎
addition of TiC particles in tungsten matrix [3,6,7,12,22–26]. Specifically, these scientific reports in the literature are principally concentrated on microstructures and hardening/embrittlement, i.e., a fewer radiation-induced defects, a lower density of blisters and a lower surface cracks [3,7,12,22,24,25], the decrease of radiation hardening [3,6,7,24,26], and the improved resistance to recrystallization embrittlement [6,7,23]. Nevertheless, regarding the cohesion and tensile properties of W-TiC system after irradiation, there is not any report so far in the literature. By means of first-principle calculations based on density functional theory [37,38], the present study is, therefore, dedicated to systematically investigate the stress-strain behaviors of W-TiC interface as well as the effects of irradiation on cohesion and tensile properties of W-TiC interface. Accordingly, the W-TiC interface with the (001)/(001) orientation is purposely chosen in the present study, as this interface has a very small mismatch of 3.396% and has been observed through experimental investigations [8]. It will be shown that the present results agree well with experimental observations in the literature, and the intrinsic mechanism will be revealed in terms of electronic structures and atomic bonding, which could provide a deep understanding regarding cohesion and tensile properties of W-TiC interface under irradiation. 2. Method of calculation The present first principle calculations are carried out using Vienna ab initio simulation package (VASP) [37,38] based on density functional
Corresponding author. E-mail address: [email protected] (H.R. Gong).
https://doi.org/10.1016/j.fusengdes.2019.111353 Received 11 July 2019; Received in revised form 31 August 2019; Accepted 29 September 2019 Available online 09 October 2019 0920-3796/ © 2019 Elsevier B.V. All rights reserved.
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¯
Fig. 1. (a) Three dimensional model and (b) x–y projection of the TiC(001)/W(001) interface. The x-axis is [100]W and [110]TiC, the y-axis is [010]W and [1 10]TiC, and the z-axis is [001]W and [001]TiC. The gray, brown, and blue spheres represent W, C, and Ti atoms, respectively.
3. Results and discussions
theory with the projector-augmented wave (PAW) method [39,40]. The exchange-correlation function is described by generalized gradient approximation (GGA) of Perdew-Burke-Enzerof (PBE) [41], and the cutoff energy of plane wave basis is 500 eV. The periodic boundary conditions are applied in three directions of the unit cell. The temperaturesmearing method of Methfessel-Paxton [42] with the energy convergence criteria of 0.01 meV and the tetrahedron method of Blöchl [43] with the energy convergence criteria of 0.001 meV are used for relaxation and static calculations, respectively. Accordingly, a 3 × 3 interface unit cell with six substrate layers (W) and six overlayers (TiC) are chosen for the TiC(001)/W(001) interface. The optimized bulk lattice constant (3.176 Å) of the substrate (W) and its BCC structure are chosen for the interface. Namely, the present TiC(001)/W(001) interface model has a unit size of 9.528 × 9.528 × 22.508 Å3 with 162 atoms, which are shown clearly in Fig. 1. For the TiC(001)/W(001) interface, the x-axis is [100]W and
3.1. Stress-strain behaviors of W-TiC interfaces It is commonly believed that the addition of TiC particles in tungsten matrix might effectively change the mechanical properties of W. As mentioned above, there are already some theoretical and experimental investigations regarding mechanical properties of the W-TiC system in the literature [2,4,8–10], while the relative magnitude of the tensile strength of the W-TiC interface from several experimental observations in the literature are quite different from each other [2,8,9], i.e., the tensile strength of W-TiC is observed to be higher [8,9] and lower [2] than that of pure W, respectively. It is, therefore, of importance to theoretically investigate this issue. After a series of calculations, Fig. 2 shows the obtained stress-strain curves of the TiC(001)/W(001) interface under tensile loading along the x ([100]W and [110]TiC) and z ([001]W and [001]TiC) directions, respectively. The corresponding curves of BCC W and B1 TiC bulks are also included in Fig. 2 for the sake of comparison. It should be pointed out that the stress-strain curve of the TiC(001)/W(001) interface, BCC W, or B1 TiC under tensile loading along the y direction is not shown, as it is equivalent to that along the x direction due to structural symmetry. One can observe from Fig. 2 that the tensile strength of W under phonon instability is very close to the climax of the stress-strain curve, suggesting that the effect of phonon instability on the ideal tensile strength of W could be neglected. On the contrary, the tensile strength of TiC caused by phonon instability along the x or z direction is lower than the corresponding ideal strength at the climax of the stress-strain curve. This feature indicates that the effect of phonon instability on the tensile strength of TiC is bigger than that of W. It should be pointed out that the obtained tensile stress of BCC W bulk along the x direction under phonon instability from the present study are 28.832 GPa, which agrees well with the corresponding calculated value of 28.86 GPa in the literature [50]. In addition, the tensile strength and critical strain of the TiC(001)/ W(001) interface along the x direction is apparently bigger than those along the z direction. Interestingly, such a feature can be also seen in B1 TiC bulk, while the stress-train curves of BCC W along the x and z directions are exactly the same due to crystal symmetry. This comparison therefore suggests that the addition of TiC fundamentally brings about the differences of the stress-strain curves of the TiC(001)/W(001) interface along the x and z directions. It could be also discerned from Fig. 2 that the critical stress of the TiC(001)/W(001) interface caused by phonon instability along the x direction is 38.596 GPa, considerably bigger than the corresponding value of 28.832 GPa for BCC W. The critical stress (30.420 GPa) of the
¯
[110]TiC, the y-axis is [010]W and [1 10]TiC, and the z-axis is [001]W and [001]TiC. Moreover, a unit cell of 4 × 4 × 4 is also constructed for BCC W and B1 TiC (a = 4.339 Å) bulks with similar settings of the above interface for the sake of comparison. For the TiC(001)/W(001) interface, the Monkhorst-Pack k-meshes of 1 × 1 × 1 and 5 × 5×5 are chosen for relaxation and static calculations, respectively. Accordingly, the interval of the tensile strain for the TiC(001)/W(001) interface is 0.01 and the stress-strain curve is derived by means of incrementally deforming the structures along the strain direction. At the same time, both the atomic basis vectors orthogonal to the applied strain and the atoms are relaxed. To ensure the continuous path of strain, the starting position at each strain step is taken from the relaxed coordinates of the previous step [44]. In order to verify the lattice instability during the process of tensile strain, the phonon spectra of both W and TiC are calculated by means of density functional perturbation theory (DFPT) method [45]. To simulate the irradiation in the interface area and keep the system from melting, the primary knock-on atom (PKA) is initiated by assigning a kinetic energy of 90 eV [46] to a W atom in the 6th layer of interface, and the moving direction of the PKA is toward the TiC lattice. Such a setting is mainly due to the well-known fact that the irradiation induced cascade in the W-TiC interface would be triggered from the dominant W phase in the actual situations [47]. After a series of test calculations, the micro-canonical ensemble (NVE) ensemble with 1000 fs is used for PKA simulations. To simulate the cohesion properties and ideal tensile properties of the interface after irradiation, the Langevin thermostat method [48,49] is used for annealing simulations from the stable temperature to 0 K. The canonical ensemble (NVT) with 1000 fs at 0 K is then performed for thermal treatment.
2
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Fig. 2. The stress-strain curves of the TiC(001)/W(001) interface along (a) the x direction ([100]W and [110]TiC) and (b) z direction ([001]W and [001]TiC) before irradiation. The corresponding curves of BCC W and B1 TiC bulks are also included for comparison.
strength of the bonds in the interface is as follows: W-C → W-W →Ti-C. In addition, the bonding strength of W-W in the interface should be stronger than that in W bulk, whereas the Ti-C bond in the interface is weaker than that in TiC bulk. Such a stronger W-W bond due to the interface formation fundamentally brings about the higher tensile strength of the W-TiC interface than those of BCC W, as shown in Fig. 2. Furthermore, Fig. 4 shows the affine deviation of W-W, Ti-C, and WC bond lengths in the TiC(001)/W(001) interface as a function of tensile strain along the z direction ([001]W and [001]TiC). It should be noted that the affine deviation is defined as the difference between the real displacement and affine displacement, and the positive value indicates that the interaction of atoms is weakened, vice versa. One can see from this figure that the affine deviation of Ti-C bond length in the interface experiences an increase as an increase of the tensile strain, while the affine deviation of W-W or W-C bond length decreases with the increase of the tensile strain. Such an opposite trend of affine deviation would be
interface along the z direction is also slightly bigger that that (28.832 GPa) of BCC W. The above features indicate that the formation of the W-TiC interface should increase the tensile strength of W, which matches well with similar experimental observations in the literature [8,9], while constrary to the other evidence from experiments [2]. According to our understanding, such an experiental controvery regarding tensile strength of W-TiC interface and BCC W might be probably due to experimental errors or contamination of the samples [2,8,9], and further experimental or theoretical studies are therefore welcome to handle this issue. To have a deep understanding of the stress-strain curves of W-TiC interfaces, Fig. 3 displays the charge density plots of TiC(001)/W(001) interface, B1 TiC bulk, and BCC W bulk. It can be discerned clearly from Fig. 3(a) that in the W-TiC interface area, the W-W bond is obviously less dense than the W-C bond, whereas denser than the Ti-C bond. This comparison indicates that the descending sequence of the bonding
Fig. 3. Charge density plots of (a) TiC(001)/W(001) interface, (b) B1 TiC bulk, and (c) BCC W bulk. 3
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Table 1 Interface energy and work of separation of TiC(001)/W(001) interface before and after irradiation. Also listed are the critical stresses of W and W-TiC interface before and after irradiation as well as the variation (Δσ ) of critical stress due to irradiation. Phases
Wsep
Eint 2
(J/m ) W
W-TiC
mainly due to the weaker Ti-C bond in the interface shown in Fig. 3(a). It therefore follows that when the tensile stress is added along the z direction perpendicular to the TiC(001)/W(001) interface, the strain would mainly happen in the TiC lattice and the final fracture should be also taken place in the TiC lattice, instead of the W lattice and W-TiC interface (figures not shown). 3.2. Cohesion and tensile properties of W-TiC interface under irradiation As mentioned above, some experimental investigations in the literature have already revealed that the addition of TiC particles could improve the irradiation resistance of tungsten alloys, i.e., the lower radiation-induced defects, lower density of blisters, lower surface cracks, and higher resistance to irradiation embrittlement and irradiation hardening [3,6,7,23,24,26]. As to the cohesion and tensile properties of W-TiC system after irradiation, however, there is not any report so far in the literature. The present first principles calculation is therefore dedicated to comparatively investigate the cohesion and tensile properties of W-TiC interface and pure W under irradiation. The work of separation (Wsep ) and interface energy (Eint ) of W-TiC interface before and after irradiation are first calculated by the following formulas [14,15]:
EW + ETiC − Etot 2A
(1)
Eint =
Etot − Ew − bulk − ETiC − bulk 2A
(2)
where EW and ETiC represent total energies of pure W and TiC surface layers after removing the TiC and W layers, respectively; Etot , Ew − bulk , and ETiC − bulk are total energies of TiC(001)/W(001) interface and bulk energies of W and TiC layers, respectively, and A is the area of the TiC(001)/W(001) interface. Consequently, the derived Wsep and Eint values of TiC(001)/W(001) interface before and after irradiation are summarized in Table 1. To find out the effects of irradiation on tensile properties of W-TiC interface, Fig. 5 displays the calculated stress-strain curves of W-TiC interface and W before and after irradiation upon tensile loading along the x ([100]W and [110]TiC) and z directions ([001]W and [001]TiC). The critical stresses of W and W-TiC interface from Fig. 5 are thus shown in Table 1. In addition, the variation (Δσ ) of critical stresses due to irradiation is defined as:
Δ σ=
σa − σb σb
5.220 4.640
(J/m )
0.865 2.285
x direction
z direction
28.832 24.377 −15.45% 38.596 27.094 −29.80%
28.832 24.377 −15.45% 30.420 20.535 −32.50%
values of Δσ values are also listed in Table 1. Several characteristics could be discerned from Fig. 5 and Table 1. Firstly, the Wsep value (4.640 J/m2) of the irradiated TiC(001)/W(001) interface becomes lower than the corresponding value of 5.220 J/m2 before irradiation, and the interface energy (2.285 J/m2) of the irradiated TiC(001)/W(001) interface is higher than that (0.865 J/m2) of the interface before irradiation. These comparisons imply that irradiation should have an important effect to reduce the cohesion strength and interface stability of the TiC(001)/W(001) interface. The fundamental mechanism of such a decrease will be revealed later in the following paragraphs. Secondly, the critical stresses and strains of both W-TiC interface and pure W after irradiation under tensile loading along the x or z direction are lower than the corresponding values before irradiation, respectively. In other words, irradiation would reduce tensile strength and ductility of both W-TiC interface and pure W. Interestingly, the decrease of critical stress (Δσ ) of the W-TiC interface due to irradiation seems much bigger than the corresponding value of pure W. Thirdly, the critical stress (27.094 GPa) of the W-TiC interface after irradiation under tensile loading along the x direction is higher than the corresponding value (24.377 GPa) of pure W. On the contrary, the critical stress (20.535 GPa) of the W-TiC interface after irradiation under tensile loading along the z direction is lower than the corresponding value (24.377 GPa) of pure W. These characteristics suggest that the addition of TiC could improve the tensile strength of W after irradiation under tensile loading along the direction parallel to the interface, while decrease the tensile strength of irradiated W under tensile loading along the direction perpendicular to the interface. It should be noted that the above observation is derived when the irradiation is performed under the low energy (90 eV) of PKA. It is of importance to have a deep understanding of the above theoretical observations in terms of atomic bonding. Accordingly, Fig. 6 shows the atomic configurations of the TiC(001)/W(001) interface after irradiation. One can observe clearly from this figure that some carbon clusters have been formed in the W-TiC interface due to irradiation, which is consistent with similar experimental observation in the literature [51]. These carbon clusters imply that some W-C and Ti-C bonds in the interface area shown in Fig. 3 should have been broken due to irradiation. Such a breaking of W-C bonds would intrinsically bring about the decrease of cohesion strength and interface stability of the W-TiC interface as mentioned above. The debonding of the Ti-C bonds due to irradiation should also induce a bigger decrease of critical stresses of the W-TiC interface as shown in Table 1. Finally, we turn to discuss a little bit about the different effects of TiC on tensile strength of irradiated W, i.e., the addition of TiC could increase the critical stress of irradiated W along the x direction parallel to the interface, whereas decrease the critical stress along the z direction perpendicular to the interface. According to our understanding, when loading is along the x direction parallel to the interface, the tensile strength of the W-TiC interface should be determined by the
Fig. 4. Affine deviation of W-W, Ti-C, and W-C bonds length in the TiC(001)/W (001) interface as a function of tensile strain along the z direction ([001]W and [001]TiC).
Wsep =
before irradiation after irradiation Δσ before irradiation after irradiation Δσ
Critical stress (GPa) 2
(3)
Where σa and σb are the critical stresses of W-TiC interface or pure W after and before irradiation, respectively. Consequently, the obtained 4
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Fig. 5. Stress-strain curves of W-TiC interface and W before and after irradiation upon tensile loading along the (a) x direction ([100]W and [110]TiC) and (b) z direction ([001]W and [001]TiC).
Fig. 6. Atomic configurations of the TiC(001)/W(001) interface after irradiation. The gray, brown, and blue spheres represent W, C, and Ti atoms, re¯
spectively. The x-axis is [100]W and [110]TiC, the y-axis is [010]W and [1 10]TiC, and the z-axis is [001]W and [001]TiC.
strong phase (TiC) as W and TiC are forced to deform together [47,52]. That is to say, the much higher strength of TiC along the x direction shown in Fig. 2(a) fundamentally brings about the increase of the tensile strength of irradiated W along the x direction. On the other hand, when loading is along the z direction perpendicular to the interface, the deformation of the W-TiC interface occurs mainly in the TiC part, and Fig. 7 displays the fracture position of TiC in the TiC(001)/W(001) interface after irradiation upon tensile loading along the z direction at a strain of 12.683%. Such a failure of TiC in the W-TiC interface along the z direction would be mainly attributed to the very close tensile strength of W and TiC shown in Fig. 2(b), the weaker Ti-C bond in the interface area revealed from Fig. 3, and the breaking of some Ti-C bonds due to irradiation displayed in Fig. 6. It therefore follows that the irradiated TiC should be weaker than the irradiated W in the W-TiC interface upon loading along the z direction, and the weaker TiC intrinsically causes the decrease of tensile strength of W along the z direction.
Fig. 7. Atomic configurations of the TiC(001)/W(001) interface after irradiation upon tensile loading along the z direction ([001]W and [001]TiC) at a strain of 12.683%. The gray, brown, and blue spheres represent W, C, and Ti atoms, respectively.
4. Conclusions First-principle calculations have been used to investigate the stressstrain behaviors of W-TiC interface as well as the effects of irradiation on cohesion and tensile properties of W-TiC interface. It is found that the formation of the W-TiC interface increases the tensile strength of W due to a stronger W-W bond in the interface, and the W-W bond is weaker and stronger than the W-C and Ti-C bonds in the interface area, respectively. Irradiation would reduce tensile strength of both W-TiC interface and pure W, while the decrease of critical stress of the W-TiC interface due to irradiation seems much bigger than that of pure W. Interestingly, TiC could increase and decrease the tensile strength of W 5
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after irradiation under tensile loading along the x and z directions, respectively. The derived results are in good agreement with experimental observations in the literature, and the intrinsic mechanism has been revealed in terms of electronic structure and atomic bonding, which could provide a deep understanding regarding cohesion and tensile properties of W-TiC interface under irradiation.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This research work was supported by National Natural Science Foundation of China (Grant No. 51534009), Project supported by the Fundamental Research Funds for the Central Universities of Central South University (No. 2018zzts126) and Project supported by State Key Laboratory of Powder Metallurgy, Central South University, Changsha, China. References [1] Z. Oksiuta, K. Perkowski, M. Osuchowski, M. Zalewska, M. Andrzejczuk, Microstructure and thermal properties of mechanically alloyed W-1% TiC powder consolidated via two-step HIPping, Fusion Eng. Des. 126 (2018) 51–58. [2] S. Lang, Q. Yan, N. Sun, X. Zhang, L. Deng, Y. Wang, C. Ge, Microstructure, basic thermal–mechanical and Charpy impact properties of W-0.1 wt.% TiC alloy via chemical method, J. Alloys. Compd. 660 (2016) 184–192. [3] H. Kurishita, Y. Amano, S. Kobayashi, K. Nakai, H. Arakawa, Y. Hiraoka, T. Takida, K. Takebe, H. Matsui, Development of ultra-fine grained W–TiC and their mechanical properties for fusion applications, J. Nucl. Mater. 367 (2007) 1453–1457. [4] H. Kurishita, S. Matsuo, H. Arakawa, M. Narui, M. Yamazaki, T. Sakamoto, S. Kobayashi, K. Nakai, T. Takida, K. Takebe, High temperature tensile properties and their application to toughness enhancement in ultra-fine grained W-(0-1.5) wt % TiC, J. Nucl. Mater. 386 (2009) 579–582. [5] S. Lang, Q. Yan, N. Sun, X. Zhang, C. Ge, Effects of TiC content on microstructure, mechanical properties, and thermal conductivity of W-TiC alloys fabricated by a wet-chemical method, Fusion Eng. Des. 121 (2017) 366–372. [6] H. Kurishita, S. Matsuo, H. Arakawa, T. Sakamoto, S. Kobayashi, K. Nakai, T. Takida, M. Kato, M. Kawai, N. Yoshida, Development of re-crystallized W–1.1%TiC with enhanced room-temperature ductility and radiation performance, J. Nucl. Mater. 398 (2010) 87–92. [7] M. Fukuda, A. Hasegawa, T. Tanno, S. Nogami, H. Kurishita, Property change of advanced tungsten alloys due to neutron irradiation, J. Nucl. Mater. 442 (2013) S273–S276. [8] S. Miao, Z. Xie, T. Zhang, X. Wang, Q. Fang, C. Liu, G. Luo, X. Liu, Y. Lian, Mechanical properties and thermal stability of rolled W-0.5 wt% TiC alloys, Mater. Sci. Eng., A 671 (2016) 87–95. [9] P.N. Browning, S. Alagic, A. Kulkarni, L. Matson, J. Singh, Room and ultrahigh temperature structure-mechanical property relationships of tungsten alloys formed by field assisted sintering technique (FAST), Mater. Sci. Eng., A 674 (2016) 701–712. [10] X.Y. Tan, P. Li, L.M. Luo, Q. Xu, K. Tokunaga, X. Zan, Y.C. Wu, Effect of secondphase particles on the properties of W-based materials under high-heat loading, Nucl. Mater. Energy 9 (2016) 399–404. [11] C.Y. Wu, L. Sun, C.P. Liang, H.R. Gong, M.L. Chang, D.C. Chen, Electronic structures and thermoelectric properties of polytype phases of bismuth, J. Phys. Chem. Solids 134 (2019) 52–57. [12] Q. Xu, X.Y. Ding, L.M. Luo, M. Miyamoto, M. Tokitani, J. Zhang, Y.C. Wu, Thermal stability and evolution of microstructures induced by He irradiation in W–TiC alloys, Nucl. Mater. Energy 15 (2018) 76–79. [13] L. Chen, L. Xiong, D.S. Li, H.R. Gong, First-principles calculation of Zr doping on cohesion properties of TiC/W interfaces, Fusion Eng. Des. 125 (2017) 85–88. [14] J.W. Wang, J.L. Fan, H.R. Gong, Effects of Zr alloying on cohesion properties of Cu/ W interfaces, J. Alloys. Compd. 661 (2016) 553–556. [15] D.Y. Dang, L.Y. Shi, J.L. Fan, H.R. Gong, First-principles study of W–TiC interface cohesion, Surf. Coat. Technol. 276 (2015) 602–605. [16] L. Chen, W. Qian, X. Lei, H.R. Gong, Mechanical properties and point defects of MC (M=Ti, Zr) from first-principles calculation, J. Alloys. Compd. 747 (2018) 972–977. [17] L.C. Liu, H.R. Gong, S.F. Zhou, X. Gong, Adsorption, diffusion, and permeation of hydrogen at PdCu surfaces, J. Membr. Sci. (2019) 117206. [18] J. Qian, C.Y. Wu, H.R. Gong, S.F. Zhou, Cohesion properties of W-ZrC interfaces from first principles calculation, J. Alloys. Compd. 768 (2018) 387–391. [19] Q.Y. Hou, L.M. Luo, Z.Y. Huang, P. Wang, T.T. Ding, Y.C. Wu, Comparison of W–TiC composite coatings fabricated by atmospheric plasma spraying and supersonic atmospheric plasma spraying, Fusion Eng. Des. 105 (2016) 77–85.
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